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Unformatted text preview: CSE541 EXERCISE 1 SOLUTIONS QUESTION 1 Describe a difference between logical and semantical paradoxes. Logical paradoxes (antinomies) are paradoxes concerning the notion of a set. Example: Russel paradox. Consider the set A of all those sets X such that X is not a member of X. Clearly, by definition, A is a member of A if and only if A is not a member of A. So, if A is a member of A, the A is also not a member of A; and if A is not a member of A, then A is a member of A. In any case, A is a member of A and A is not a Semantical paradoxes (antinomies) are paradoxes that deal with notion of truth, provability, and hence with logic. Example: The Liar Paradox. A man says: I am lying . If he is lying, then what he says is true, and so he is not lying. If he is not lying, then what he says is not true, and so he is lying. In any case, he is lying and he is not lying. QUESTION 2 1. We translate our statement From the fact that it is possible that Chris is not a boy we deduce that it is not possible that Chris is not a boy or, if it is possible that Chris is not a boy, then it is not necessary that Anne is pretty. into a formula (i) A 1 ∈ F 1 of a language L {¬ , C , I , ∩ , ∪ , ⇒} as follows. Propositional Variables: a,b . a denotes statement: Chris is a boy , b denotes a statement: Anne is pretty ....
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This note was uploaded on 02/12/2011 for the course CSE 541 taught by Professor Bachmair,l during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 Bachmair,L
 Computer Science

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